Difference between revisions of "Crack Settings"
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<math>\cos\theta = {3K_{II}^2 + K_{I}\sqrt{K_I^2+8K_{II}^2} \over K_I^2+9K_{II}^2} \quad {\rm and} \quad | <math>\cos\theta = {3K_{II}^2 + K_{I}\sqrt{K_I^2+8K_{II}^2} \over K_I^2+9K_{II}^2} \quad {\rm and} \quad | ||
\sin\theta = \mp\sqrt{1- | \sin\theta = \mp\sqrt{1-\cos^2\theta} = \mp\left | {K_{II}\over K_I}(3\cos\theta - 1)\right|</math> | ||
The second terms in negative or positive depending on K<sub>II</sub> being positive or negative. | The second terms in negative or positive depending on K<sub>II</sub> being positive or negative. | ||
Revision as of 08:22, 19 September 2013
This section needs writing. Below are some items that will be used or move else where.
In max energy release rate (or max hoop stress), the crack direction is at angle θ (which is ccw from self similar growth) and obeys
[math]\displaystyle{ \cos\theta = {3K_{II}^2 + K_{I}\sqrt{K_I^2+8K_{II}^2} \over K_I^2+9K_{II}^2} \quad {\rm and} \quad \sin\theta = \mp\sqrt{1-\cos^2\theta} = \mp\left | {K_{II}\over K_I}(3\cos\theta - 1)\right| }[/math]
The second terms in negative or positive depending on KII being positive or negative.